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This is a repository copy of Modelling the feedbacks between mass balance, ice flow and debris transport to predict the response to climate change of debris-covered glaciers in theHimalaya.
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Article:
Rowan, A.V., Egholm, D.L., Quincey, D.J. et al. (1 more author) (2015) Modelling the feedbacks between mass balance, ice flow and debris transport to predict the response to climate change of debris-covered glaciers in the Himalaya. Earth and Planetary Science Letters, 430. 427 - 438. ISSN 0012-821X
https://doi.org/10.1016/j.epsl.2015.09.004
[email protected]://eprints.whiterose.ac.uk/
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1
Modelling the feedbacks between mass balance, ice flow and debris 1
transport to predict the response to climate change of debris-covered 2
glaciers in the Himalaya 3
4
Ann V. Rowan1*, David L. Egholm2, Duncan J. Quincey3, Neil F. Glasser4 5
6
1Department of Geography, University of Sheffield, Sheffield, S10 2TN, UK 7
2Department of Geoscience, Aarhus University, Aarhus C, Denmark. 8
3School of Geography, University of Leeds, Leeds, LS2 9JT, UK 9
4Department of Geography and Earth Sciences, Aberystwyth University, Aberystwyth, SY23 10
3DB, UK 11
12
13
*Corresponding author: [email protected] 14
2
Abstract 15
Many Himalayan glaciers are characterised in their lower reaches by a rock debris layer. This 16
debris insulates the glacier surface from atmospheric warming and complicates the response 17
to climate change compared to glaciers with clean-ice surfaces. Debris-covered glaciers can 18
persist well below the altitude that would be sustainable for clean-ice glaciers, resulting in 19
much longer timescales of mass loss and meltwater production. The properties and evolution 20
of supraglacial debris present a considerable challenge to understanding future glacier 21
change. Existing approaches to predicting variations in glacier volume and meltwater 22
production rely on numerical models that represent the processes governing glaciers with 23
clean-ice surfaces, and yield conflicting results. We developed a numerical model that 24
couples the flow of ice and debris and includes important feedbacks between debris 25
accumulation and glacier mass balance. To investigate the impact of debris transport on the 26
response of a glacier to recent and future climate change, we applied this model to a large 27
debris-covered Himalayan glacier—Khumbu Glacier in Nepal. Our results demonstrate that 28
supraglacial debris prolongs the response of the glacier to warming and causes lowering of 29
the glacier surface in situ, concealing the magnitude of mass loss when compared with 30
estimates based on glacierised area. Since the Little Ice Age, Khumbu Glacier has lost 34% 31
of its volume while its area has reduced by only 6%. We predict a decrease in glacier volume 32
of 8–10% by AD2100, accompanied by dynamic and physical detachment of the debris-33
covered tongue from the active glacier within the next 150 years. This detachment will 34
accelerate rates of glacier decay, and similar changes are likely for other debris-covered 35
glaciers in the Himalaya. 36
37
1. Introduction 38
Glaciers in the Himalaya are rapidly losing mass (Bolch et al., 2012). However, data 39
describing past and present glacier volumes are scarce, resulting in varying predictions of 40
future glacier volumes (Cogley, 2011; Kääb et al., 2012). To improve predictions of how 41
Himalayan glaciers will decline through the 21st Century and the impact on Asian water 42
resources, we need to quantify the processes that drive glacier change (e.g. Immerzeel et al., 43
2013; Pellicciotti et al., 2015; Ragettli et al., 2015; Shea et al., 2015). Changes in glacier 44
volume are driven by climate variations, particularly changes in atmospheric temperature and 45
precipitation amount, and modified by ice flow (Bolch et al., 2012; Kääb et al., 2012). The 46
lower portions of clean-ice glaciers lose mass rapidly during periods of warming. As glaciers 47
recede to higher elevations, a new equilibrium state between this smaller glacier and the 48
3
warmer climate may be established. Numerical modelling is required to understand the 49
processes that cause glaciers to change because we cannot rely simply on the extrapolation of 50
present-day trends. Previous studies of Himalayan glaciers using models designed for clean-51
ice glaciers resulted in predictions of widespread rapid deglaciation (e.g. Shea et al., 2015). 52
However, debris-covered glaciers respond differently to warming because debris insulates the 53
ice surface (Jouvet et al., 2011; Kirkbride and Deline, 2013; Pellicciotti et al., 2015; Østrem, 54
1959). Debris-covered glaciers lose most mass by surface lowering rather than terminus 55
recession (Hambrey et al., 2008). Debris-covered glaciers can persist at lower elevations than 56
would be possible for an equivalent clean-ice glacier even when dramatically out of 57
equilibrium with climate (Anderson, 2000; Benn et al., 2012). As glaciers lose mass 58
preferentially from areas of clean ice and mass loss results in the melt-out of englacial debris, 59
debris coverage will increase as a glacier shrinks (Bolch et al., 2008; Kirkbride and Deline, 60
2013; Thakuri et al., 2014). Therefore, predicting the future of the Himalayan cryosphere and 61
water resources depends on understanding the impacts of climate change on debris-covered 62
glaciers. 63
64
Debris on glacier tongues is derived from surrounding hillslopes and is transported 65
englacially before resurfacing in the ablation zone (Fig. 1a). In times negative mass balance, 66
velocities decline and debris thickness at the ice surface increases (Kirkbride and Deline, 67
2013) (Fig. 1b). A thin layer of rock debris (0.01–0.1 m) enhances glacier surface ablation by 68
reducing albedo, whereas thicker rock debris reduces ablation by insulating the surface 69
(Mihalcea et al., 2008; Nicholson and Benn, 2006; Østrem, 1959). Thick supraglacial debris 70
causes a reversal of the mass balance gradient, with higher ablation rates upglacier than at the 71
terminus leading to reduced driving stresses and ice flow (Jouvet et al., 2011; Quincey et al., 72
2009). Spatial heterogeneity in debris thickness results in differential surface ablation and the 73
formation and decay of ice cliffs and supraglacial ponds that locally enhance ablation (Reid 74
and Brock, 2014; Sakai et al., 2000). An obstacle to understanding the behaviour of debris-75
covered glaciers lies in quantifying the highly variable distribution of debris across the 76
glacier surface and how this differs between glaciers. Supraglacial debris distribution and 77
thickness are difficult to determine remotely and laborious to measure directly (Mihalcea et 78
al., 2008; Nicholson and Benn, 2006; Reid et al., 2012), particularly over more than one 79
glacier (Pellicciotti et al., 2015). A further challenge to predicting the response of debris-80
covered glaciers to climate change is understanding not only the distribution of debris on a 81
glacier surfaces, but also how this varies over time. 82
4
83
In the Himalaya, 14–18% of the total glacierised area is debris-covered (Kääb et al., 2012) 84
increasing to about 36% in the Everest region of Nepal which contains some of the longest 85
debris-covered glacier tongues in the world are found (Nuimura et al., 2012; Thakuri et al., 86
2014). Where debris cover on an individual glacier exceeds 40% of the total area mass loss is 87
mainly by terminus stagnation rather than recession (which requires a loss of mass whilst 88
maintaining flow towards the migrating terminus) (Immerzeel et al., 2013; Quincey et al., 89
2009). Some Himalayan glaciers are over 50% debris covered (Ragettli et al., 2015) and 90
debris is sufficiently thick to reduce rather than enhance ablation (Benn et al., 2012; Bolch et 91
al., 2008; Nicholson and Benn, 2006). In the Everest region of Nepal, 70% of the glacierised 92
area comprises just 40 of 278 glaciers, and these large glaciers are generally debris covered 93
(Thakuri et al., 2014) (Fig. 2a). Glaciers in the Everest region last advanced around 0.5 ka, a 94
period referred to as the Little Ice Age (LIA) but distinct from the European event of the 95
same name (Owen et al., 2009; Richards et al., 2000). Since the LIA, Everest-region glaciers 96
have consistently lost mass (Kääb et al., 2012; Nuimura et al., 2012). Between 1962 and 97
2011, the proportion of Everest region glaciers covered by rock debris has doubled due to 98
ongoing mass loss (Thakuri et al., 2014). 99
100
The future of debris-covered glaciers worldwide is uncertain due to the limitations of our 101
knowledge about the distribution of supraglacial debris and how this evolves over time. 102
Existing models designed for clean-ice glaciers or static assumptions that describe only the 103
present state of the glacier are difficult to extrapolate under a changing climate. Here, we use 104
a novel glacier model that includes the self-consistent development of englacial and 105
supraglacial debris and reproduces the feedbacks among mass-balance, ice-flow and debris 106
transport to investigate how debris modifies the behaviour of a Himalayan glacier in response 107
to climate change. As an example of how many debris-covered Himalayan glaciers respond 108
to climate change, we applied this model to the evolution of Khumbu Glacier in the Everest 109
region of Nepal from the Late Holocene advance (1 ka) to AD2200. 110
111
2. Khumbu Glacier, Nepal 112
Khumbu Glacier is a large debris-covered glacier in the Everest region (Fig. 2), with a length 113
of 15.7 km and area of 26.5 km2. The Changri Nup and Changri Shar Glaciers were 114
tributaries of Khumbu Glacier during the LIA but have since detached. The equilibrium line 115
altitude (ELA) estimated from mass balance measurements made in 1974 and 1976 is 5600 m 116
5
(Benn and Lehmkuhl, 2000; Inoue, 1977; Inoue and Yoshida, 1980). More recent studies 117
have placed the ELA of Khumbu Glacier at 5700 m around AD2000 (Bolch et al., 2011) 118
within the icefall that links the accumulation area in the Western Cwm to the glacier tongue 119
(Fig. 3). The ELA may have increased due to atmospheric warming of about 0.9°C between 120
1994 and 2013 (Salerno et al., 2014). 121
122
The active part of Khumbu Glacier (the area exhibiting ice flow) receded towards the base of 123
the icefall since the end of the LIA while the total glacier length remained stable. Feature-124
tracking observations of velocities define the length of the active glacier as 10.3 km (62% of 125
the LIA glacier length) (Fig. 4). Decaying ice at the terminus beneath debris several metres 126
thick indicates terminus recession of less than 1 km since the LIA (Bajracharya et al., 2014). 127
We divide Khumbu Glacier into two parts based on observations of glacier dynamics; (1) the 128
active glacier where velocities range from 10 m to 70 m a-1 and mass is replenished from the 129
accumulation zone, and (2) the decaying tongue that no longer exhibits ice flow of more than 130
a few m a-1. Similar behaviour is reproduced by our glacier model and observed for many 131
glaciers in the Everest region (Quincey et al., 2009). 132
133
3. Methods 134
3.1 Bed topography 135
Ice thickness for Khumbu Glacier (Fig. 3) has been measured along seven transects down-136
glacier from the icefall using radio-echo sounding was 440 ± 20 m at 0.5 km below the icefall 137
close to Everest Base Camp, decreasing to less than 20 m at 4930 m at 2 km up-glacier of the 138
terminus (Gades et al., 2000). Gravity observations gave an ice thickness of 110 m adjacent 139
to Lobuche and 440 m adjacent to Gorak Shep (Moribayashi, 1978). No data exist above the 140
icefall. Ice thickness can be estimated by assuming that glacier ice behaves as a perfectly 141
plastic material such that thickness (h) is determined by surface slope (Į) and basal shear 142
stress (IJb) (Nye, 1952): 143
144
h = そ * (IJb / f * と * g * sin(g)) 145
146
where ȡ is the density of glacier ice, and g is acceleration due to gravity. A shape factor (f) 147
describes the aspect ratio of the cross-section of a valley glacier (Nye, 1952), and a down-148
glacier thinning factor (そ) describes the long profile: 149
150
6
そ = 1 – a * xb 151
152
where a is a constant accounting for the length of the glacier, x is the flowline distance from 153
the headwall and b describes where thinning first occurs along the flowline. We estimated the 154
thickness of Khumbu Glacier at 35 regularly-spaced transects perpendicular to the central 155
flowline. Glacier topography was described using the ASTER GDEM 2011 Digital Elevation 156
Model (DEM) and the GLIMS outline (GLIMS et al., 2005). Values for IJb, f and そ were 157
determined by tuning against observations resulting in a mean IJb value of 150 kPa. Subglacial 158
bedrock topography was described by subtracting the interpolated ice thickness from the 159
DEM, smoothing and resampling to 100-m grid spacing. 160
161
3.2 Glacier topography 162
Topographic profiles were measured using a DEM with a 10-m grid spacing generated from 163
ALOS PRISM imagery acquired in 2006 (Fig. 2b). Glacier topography was calculated 164
perpendicular to the central flowline by taking the mean of a 200-m wide moving window. 165
The LIA glacier surface was reconstructed from the elevation of lateral and terminal moraine 166
crests which are preserved below the icefall (Fig. 2a). The LIA moraine crest was defined by 167
taking the maximum of a 300-m wide moving window centred on the moraine, and verified 168
in the field using a Garmin GPSmap 62s handheld unit (Fig 2c). There are no indicators of 169
past glacier topography above the icefall, so model simulations were fitted to the available 170
data from the ablation zone. 171
172
3.3 Glacier dynamics 173
Glacier velocities (i.e. surface displacements) were calculated using the panchromatic bands 174
of multi-temporal Landsat Operational Land Imager imagery and a Fourier-based cross-175
correlation feature tracking method (Luckman et al., 2007). The images were first co-176
registered with sub-pixel accuracy using large feature (128 x 128 pixels; 1920 m square) and 177
search (256 x 256 pixels; 3840 m square) windows focusing on non-glacierised areas. Glacier 178
displacements were then calculated using finer feature and search windows of 48 x 48 pixels 179
(720 m square) and 64 x 64 pixels (960 m square). Sufficiently robust correlations were 180
accepted on the strength of their signal-to-noise ratio and matches above an extreme 181
threshold of 100 m a-1 were removed as blunders. The remaining displacements were 182
converted to annual velocities assuming no seasonal variability in flow. Errors in the velocity 183
data comprise mismatches associated with changing surface features between images, and 184
7
any inaccuracy in the image co-registration. Given that the glacier is slow-flowing (and thus 185
features do not change rapidly), and that the images were co-registered to a fraction of a 186
pixel, we estimate a maximum theoretical error of one pixel per year (i.e. 15 m). Empirically 187
measured displacements in stationary areas adjacent to the glacier suggest the real error is 188
around half this (i.e. 7–8 m a-1). 189
190
3.4 Numerical modelling 191
We used the ice model iSOSIA (Egholm et al., 2011) with a novel description of debris 192
transport that represents the self-consistent development of englacial and supraglacial debris 193
and reproduces the feedbacks amongst mass-balance, ice-flow and debris accumulation. 194
iSOSIA is a higher-order shallow-ice model, which in contrast to standard shallow-ice 195
approximation (SIA) models includes the effects of longitudinal and transverse stress 196
gradients. This makes iSOSIA more accurate than SIA models in settings where flow 197
velocities can vary over short distances, such as in steep and rugged terrains of alpine glaciers 198
(Egholm et al., 2011). Supraglacial debris across Himalayan glaciers is generally decimetres 199
to metres thick and acts to reduce rather than enhance ablation. Moreover, where debris cover 200
is thin in the upper part of the ablation zone of Khumbu Glacier, similar ablation rates are 201
observed for surfaces both with and without debris (Inoue and Yoshida, 1980). Therefore, 202
ablation beneath supraglacial debris was calculated using an exponential function that gave a 203
halving of ablation beneath 0.5 m of debris and assuming minimal ablation beneath a debris 204
layer with a thickness exceeding 1.0 m, in line with values calculated for neighbouring 205
Ngozumpa Glacier (Nicholson and Benn, 2006). 206
207
Transport of debris within and on top of the glacier was modelled as an advection problem 208
assuming that the ice passively transports the debris. Internal ice deformation and basal 209
sliding drive ice flow in iSOSIA and the depth-averaged flow velocity is therefore 210
211
四拍 噺 四拍鳥 髪 四長 212
213
The velocity due to ice deformation, 憲博鳥 ┸ is approximated as a tenth-order polynomial 214
function of ice thickness with coefficients that depend on ice surface slope and bed slope as 215
well as longitudinal stress and stress gradients (Egholm et al., 2011). 216
217
8
Basal sliding is assumed to scale with the basal shear stress according to the following 218
empirical sliding model (Budd and Keage, 1979): 219
220 憲長 噺 稽鎚酵長陳軽勅
221
where 軽勅 is the effective pressure at the bed, and 稽鎚 噺 ね 抜 など貸替 m a-1 Pa-1 and 兼 噺 に are 222
constants. The basal shear stress is the bed-parallel stress vector at the base of the ice, which 223
is computed by projecting the full stress tensor at the base of the ice onto the glacier bed. The 224
shear stress is therefore sensitive to ice thickness, ice surface slope, local ice velocity 225
variation, as well as bed slope orientation (Egholm et al., 2011). The effective pressure was 226
assumed to be 20% of the ice overburden pressure. This standard approach (e.g. 227
Bindschadler, 1983; Braun et al., 1999; Egholm et al., 2012; Kessler et al., 2008) to 228
modelling basal sliding in alpine glaciers ignores the detailed distribution of water pressure as 229
well as ice-bed cavitation, which are both elements that we have no means of calibrating 230
empirically for Khumbu Glacier. We note that the distribution of sliding is thus considered 231
uncertain, also because the two sliding parameters 稽鎚 and 兼 are difficult to constrain 232
empirically; according to Budd et al. (1979), 兼 should vary between 1 and 3. On the other 233
hand, variations in sliding rate do not significantly influence our modelling results as long as 234
ice, and thus also englacial debris, is transported from the accumulation zone to the ablation 235
zone by either basal sliding or internal ice creep. 236
237
The debris concentration, c, at any point within the ice was updated through time, t, using the 238
following equation for debris advection: 239
240 項潔項建 噺 伐椛 ゲ 岶潔四岼 241
where u is the three-dimensional ice velocity vector. The equation is based on the assumption 242
that debris is transported passively with the ice, and hence that any change in debris 243
concentration in a point is controlled by the flux of debris and ice to and from that point. For 244
example, at the surface in the ablation zone, debris concentration generally increases over 245
time because melting of ice causes the total influx of ice by flow to be positive. Debris may 246
also accumulate along the base of the ice, because basal melting, controlled by the excess 247
9
heat at the glacier bed (Egholm et al., 2012), drives ice towards the bed. However, most 248
debris follows a concave path from the ice surface in the accumulation zone, down to some 249
depth within the glacier, and then back to the glacier surface in the ablation zone. As a 250
boundary condition to the above equation, we assumed that debris is fed to the surface of the 251
glacier in the accumulation zone and that csa=0.001 (the concentration of debris at the ice 252
surface) is constant across the accumulation area. Debris in the high parts of Khumbu Glacier 253
is likely transported to the glacier by avalanches, and the high energy of the avalanches can 254
spread snow and debris across wide areas of the glacier surface. Without detailed knowledge 255
of the distribution and frequency of avalanches, we used a constant surface debris 256
concentration in the accumulation zone as the simplest possible boundary condition. We note, 257
however, that because localised quantities of debris in the accumulation zone have a tendency 258
of diffusing during transport in the glacier, the wide-spread distribution of debris near the 259
terminus of the glacier is largely insensitive to variations in the debris input distribution of 260
the accumulation zone. The order of csa was roughly estimated by considering the total area 261
of the surrounding ice-free hillslopes and assuming that the mean erosion rate is about 1 mm 262
a-1. The total hillslope sediment production was then uniformly distributed across the area of 263
the ice accumulation zone. We note that sediment production from these hillslopes varies 264
through time in response to variations in rock uplift and climate change (Scherler et al., 265
2011). However, our model experiments focus on the spatial patterns of debris distribution 266
and disregard any temporal evolution of debris production. The rate of debris input used here 267
should consequently only be regarded as a first-order estimate. 268
269
Debris transport was modelled using a three-dimensional grid. iSOSIA is a depth-integrated 270
2-D model, but for the purpose of tracking the three-dimensional debris transport, the 271
thickness of the ice was divided into 20 layers representing the vertical dimension of the 3-D 272
grid structure. iSOSIA only computes depth-averaged velocity components. However, to 273
capture velocity variations at depth within the ice we reconstructed in every time step the full 274
three-dimensional velocity field of the glacier. The vertical variation of velocity components 275
was derived from the assumption that the horizontal ice velocity caused by viscous ice 276
deformation decays as a fourth-order polynomial down through the ice, which is valid for 277
laminar flow of ice with a stress exponent of 3 (Van der Veen, 2013; p. 77). We calibrated 278
the fourth-order polynomial to yield the correct depth-averaged velocity: 279
280
10
四岫権岻 噺 のね 釆な 伐 岾権月峇替挽 四拍 髪 四長
281
where 四拍 is the depth-averaged horizontal velocity and ub is basal sliding velocity. z is burial 282
depth below the ice surface and h is ice thickness. The internal vertical component of the ice 283
velocity, uv, was scaled linearly with accumulation/ablation at the surface (兼岌 鎚岻 and melting at 284
the glacier bed (兼岌 長岻: 285 憲塚岫権岻 噺 月 伐 権月 兼岌 鎚 髪 権月 兼岌 長
286
Melting at the bed is computed from the heat available at the bed: 287
288 兼岌 長 噺 圏長 髪 憲長 ゲ 酵長 伐 圏頂貢詣
289
where 圏長 噺 ど┻どねの W m-2 is the heat flux from the underlying crust; 憲長 ゲ 酵長 is the heat 290
produced at the bed by friction due to basal sliding; 貢 噺 ひぱど kg m-3 is the density of glacier 291
ice and 詣 噺 ぬぬね kJ kg-1 is the latent heat of ice. 圏頂 is the heat transported away from the 292
glacier bed by heat conduction in the overlying ice. It is estimated from the thermal gradient 293
at the glacier bed: 294 圏頂 噺 伐倦 項劇項権
295
and the thermal conductivity of ice, 倦 噺 に┻ね W m-1 K-1. The temperature field within the ice 296
was computed using the three-dimensional semi-implicit algorithm described by Egholm et 297
al. (2012). The rates of basal melting were typically limited to the order of 0.01 m a-1, which 298
is 1–2 orders of magnitude smaller than the rates of surface ablation. 299
300
The advection equation was integrated through time using explicit forward time stepping in 301
combination with a three-dimensional upwind finite-difference scheme. The size of the time 302
step was restricted by the Courant-Friedrichs-Lewy condition: 303
304 ッ建 判 なに ッmin憲max 305
11
where ッmin is the smallest cell-dimension (along the x, y and z axes), and 憲max is the 306
maximum ice velocity component. Time steps were by this condition restricted to 1–5 model 307
days. The iSOSIA and debris transport algorithms were parallelised using OpenMP 308
(Chapman et al., 2007), and run on 12-core CPU servers. Each simulation typically lasted 8–309
12 hours. 310
311
3.5 Experimental design 312
Simulations were made for the catchment upstream from the base of the LIA terminal 313
moraine. The DEM was constructed from data collected between AD2001 and AD2010 so 314
we place the present day at the start of this window as AD2000. Mass balance was calculated 315
assuming linear temperature-dependent rates of accumulation and ablation following those 316
measured in 1974 and 1976 (Benn and Lehmkuhl, 2000; Inoue, 1977; Inoue and Yoshida, 317
1980). An atmospheric lapse rate of –0.004°C m-1 was calculated by linear regression of 318
MODIS Terra land surface temperatures (24/02/00–31/12/06) (NASA, 2001) for the Central 319
Himalayan region (Fig. 4). Glacier advance and recession were simulated by varying ELA 320
over time. Extreme topography results in the majority of glacier mass gain by avalanching 321
rather than direct snowfall, and the avalanche contribution to mass balance was estimated as 322
75% (Benn and Lehmkuhl, 2000). We removed snow and ice from slopes exceeding 28° and 323
redistributed the total volume uniformly on the accumulation area of the glacier surface. The 324
critical slope of 28° was selected because this threshold is low enough to prevent ice 325
accumulation on slopes that are clearly ice-free today, but high enough to not limit ice 326
accumulation on the glacier surface. 327
328
3.5.1 Initial Late Holocene simulation 329
Prior to the LIA (0.5 ka), Khumbu Glacier had a slightly greater extent during the Late 330
Holocene (~1 ka) and is likely to have reached the LIA extent by the formation of high 331
moraines that enclosed the glacier and drove the ice mass to thicken (Owen et al., 2009) (Fig. 332
2a). As a starting point for our transient simulations, we reconstructed the Late Holocene 333
glacier from an ice-free domain using an ELA of 5325 m over a 5000-year period. This 334
simulation was optimised to result in a steady-state glacier that provided a good fit to the Late 335
Holocene moraines (Fig. 5). A minor recession, inferred from the position of the LIA 336
moraines inside the Late Holocene moraines, was imposed after the Late Holocene advance 337
equivalent to an increase in ELA of 50 m to 5375 m over 500 years, and supraglacial debris 338
thickened due to the reduction in debris export as glacier velocities decreased. 339
12
340
3.5.2 Simulation from the LIA to the present day 341
To simulate the LIA advance, maximum and recession, the ELA was increased from 5375 m 342
to 6000 m over 500 years. The distribution of englacial and supraglacial debris simulated for 343
the Late Holocene was used as a starting point for the LIA simulation. A range of present-day 344
ELA values (Fig. 3) was tested by comparing the simulated ice volume with observed glacier 345
topography; the best fit to the present-day ice thickness was an ELA of 6000 m. This places 346
the ELA of Khumbu Glacier at the top of the icefall rather than in the lower half as indicated 347
by recent measurements (Fig. 3). The simulated ice thicknesses were optimised to the LIA 348
moraines and the present-day glacier. This simulation ran to steady state to indicate how the 349
glacier would continue to evolve without any further change in climate. 350
351
3.5.3 Simulation from the present day to AD2200 352
Simulation of glacier change from the present day until AD2200 continued from the present-353
day simulation where the glacier was out of balance with climate. We imposed a linear rise in 354
ELA over 100 years from AD2000 to AD2100 equivalent to predicted minimum and 355
maximum warming relative to 1986–2005 by 2080–2099 of 0.9°C (increase in ELA of 225 m 356
assuming an atmospheric lapse rate of –0.004°C m-1) and 1.6°C (increase in ELA of 400 m), 357
in line with IPCC model ensemble predictions (CMIP5 RCP 4.5 scenario) (Collins et al., 358
2013). The simulation continued until AD2200 without any further change in climate. 359
360
3.6 Mass balance sensitivity 361
We tested the sensitivity of Khumbu Glacier to mass balance parameter values through the 362
LIA to the present day to assess the impact of these uncertainties on our projections for 363
AD2100. A range of present-day ELA values equivalent to a change in ELA of 150 m 364
(equivalent to ±0.3°C) produced a difference in glacier volume of 0.3 x 109 m3 (14% of 365
present-day volume) with no change in glacier length beyond the cell size of the model 366
domain (100 m). Lapse rates between –0.003°C m-1 and –0.006°C m-1 and no change in ELA 367
produced a difference in glacier volume of 0.4 x 109 m3 (19%) with no change in length. 368
Maintaining the relationship with temperature between rates of accumulation and ablation 369
whilst varying maximum values by ±10% produced a difference in glacier volume of 4.0 x 370
106 m3 (0.2%) with no change in length. 371
372
3.7 Comparison with simulations that do not transport debris 373
13
To verify the effect of supraglacial debris on glacier change, the LIA to the present day was 374
simulated: (1) without the modification of ablation beneath the debris layer, that is, assuming 375
a clean rather than debris-covered surface, and (2) with maximum ablation reduced by 50% 376
(as in Section 3.6) to compare the impact of a uniform reduction in ablation, as sometimes 377
used when clean-ice glacier models are applied to debris-covered glaciers (Fig. 6). Mass loss 378
from the clean-ice glacier greatly exceeded that from the debris-covered glacier, resulting in a 379
glacier with 16% of the present-day volume and a 6.7 km reduction in length compared to the 380
dynamic debris-covered glacier simulated for the same period. A reduction in ablation of 381
50% resulted in dramatic mass loss to 27% of present-day volume and a 4.4 km reduction in 382
length compared to the dynamic debris-covered glacier simulated for the same period. Our 383
results highlight that the change in terminus position of debris-covered glaciers in response to 384
climate change is slower than for clean-ice glaciers. Similar behaviour is observed using 1-D 385
modelling (Banerjee and Shankar, 2013) and remote-sensing observations (Kääb et al., 2012). 386
Therefore, models developed for clean-ice glaciers using a uniform reduction in ablation do 387
not reliably simulate the evolution of debris-covered glaciers. 388
389
4. Results 390
4.1 Glacier morphology 391
Reconstruction of Khumbu Glacier using moraine crests showed that, since the LIA, glacier 392
area has decreased from 28.1 km2 to 26.5 km2 (a reduction of 6%). If the glacier is considered 393
only in terms of active ice, then area has declined to 20.3 km2 (a reduction of 28%) (Fig. 4). 394
These values exclude the change in area attributed to the dislocation of the Changri Nup and 395
Changri Shar tributaries (Fig. 4). The volume of the active glacier is 1.7 x 109 m3 (50% of the 396
LIA volume). The lack of dynamic behaviour in the tongue can be observed from the relict 397
landslide material on the true left of the glacier that has not moved between 2003 and 2014 398
(Fig. 2a). Comparison of swath topographic profiles of the glacier surface and the LIA lateral 399
moraine crests (Fig. 2c) indicate mean surface lowering across the debris-covered tongue of 400
25.5 ± 10.6 m, or 0.05 ± 0.02 m a-1 since the LIA. Glacier volume decreased from 3.4 x 109 401
m3 to 2.3 x 109 m3 (66% of the LIA volume), a loss of 1.2 x 109 m3 and equivalent to 2.3 x 106 402
m3 a-1. Mean surface lowering observed between 1970 and 2007 across the ablation area was 403
13.9 ± 2.5 m (Bolch et al., 2011) suggesting that rates of mass loss have accelerated over the 404
last 50 years compared to the last 500 years, and consistent with the observed decrease in the 405
active glacier area (Quincey et al., 2009). 406
407
14
4.2 Glacier modelling 408
The initial simulation representing the Late Holocene maximum was computed from an ice-409
free domain using an ELA of 5325 m (–2.7°C relative to the present day). Debris 410
accumulated at the ice margins rather than on the glacier surface to form lateral moraines 411
(Fig. 5). 412
413
4.2.1 The Little Ice Age to the present day 414
Khumbu Glacier initially advanced during the LIA for 150 years despite the rise in ELA as 415
decreasing velocity in the tongue (Table 1) resulted in thickening supraglacial debris (Fig. 7a 416
and 7c). The large LIA moraines suggest that debris export from the glacier to the ice 417
margins declined because the glacier was impounded following the construction of these 418
moraines. This simulation reproduced this observation, and resulted in the formation of a 419
thick debris layer (Fig. 7d). The simulated LIA glacier surface provided a good fit to the LIA 420
moraine crests (Fig. 7e). The simulated glacier then lost mass by surface lowering 421
accompanied by minor terminus recession, despite the reduction in ablation beneath 422
supraglacial debris (Fig 7b and Table 1). Simulated present-day ice thicknesses were in good 423
agreement with the observed glacier surface (Fig. 7f). The maximum simulated present-day 424
ice thickness was 345 m. The mean flowline ice thickness was 168 m for the whole glacier, 425
88 m in the accumulation area and 210 m for the debris-covered tongue. Simulated velocities 426
(Table 1 and Fig. 8) reproduced the pattern and absolute values measured from remote-427
sensing observations (Fig. 4). 428
429
After the LIA maximum, simulated ice thickness declined most rapidly for the first 200 years 430
of warming followed by slightly less rapid mass loss for the following 300 years. Mean ice 431
thickness across the entire glacier decreased by 0.01 m a-1, and surface lowering was greatest 432
between 1.8 km and 3.2 km upglacier from the terminal moraine. The active glacier shrunk to 433
the observed active ice extent but did not reach steady state. The response time to reach 434
equilibrium with the present-day ELA was 1150 years, 500 years longer than the time elapsed 435
between the LIA maximum and the present day, indicating that Khumbu Glacier is out of 436
balance with climate. According to our model, Khumbu Glacier will continue to respond to 437
post-LIA warming until about AD2500 and will lose a further 0.4 x 109 km3 (18%) of ice 438
without any further change in climate. 439
440
4.2.2 Present day to AD2200 441
15
To predict glacier volume at AD2100 and AD2200, we imposed a linear rise in ELA from the 442
present day following IPCC minimum and maximum warming scenarios for AD2100 443
(Collins et al., 2013). These simulations were driven by an increase in ELA of 225 m to 6225 444
m (equivalent to warming of 0.9°C) and 400 m to 6400 m (equivalent to warming of 1.6°C) 445
over 100 years, and without a further change in climate until AD2200. Warming of 0.9°C by 446
AD2100 will result in mass loss of 0.17 x 109 km3 and warming of 1.6°C will result in mass 447
loss of 0.21 x 109 km3 (Fig. 9a and 9c), a decrease in glacier volume of between 8% and 10% 448
(Table 1). Simulated mass loss will be greatest close to the base of the icefall, where ablation 449
exceeds that occurring down-glacier beneath thicker supraglacial debris and up-glacier in the 450
Western Cwm. Supraglacial debris will expand and thicken across the glacier tongue, 451
particularly between the confluence with Changri Nup Glacier and the icefall (Fig. 9e 452
compared to Fig. 7d), reaching 1.5 m thickness at the base of the icefall. The debris-covered 453
tongue could physically detach from the base of the icefall within 150 years and persist in 454
situ while the active glacier recedes (Fig. 9b and 9d). After the physical detachment of the 455
debris-covered tongue, supraglacial debris will develop on the tongue of the active glacier 456
near the upper part of the icefall (Fig. 9f). 457
458
5. Discussion 459
5.1 Validation of model simulations 460
The present-day simulation was validated by comparison with observations of velocities, 461
mean surface elevation change and geodetic mass balance derived from satellite imagery. The 462
simulated present-day maximum flowline velocity was 59 m a-1 and the mean was 9 m a-1 463
(Fig. 8a and 8b). The mean simulated velocity above the base of the icefall was 24 m a-1, and 464
the mean velocity of the debris-covered tongue below the icefall was 2 m a-1. These 465
simulated velocities are in good agreement with those measured using feature tracking (Fig. 466
4), which give a maximum flowline velocity of 67 m a-1 and a mean of 16 m a-1. The mean 467
measured velocity above the base of the icefall was 25 m a-1, and the mean velocity of the 468
debris-covered tongue was 9 m a-1. The measured velocity of the tongue is within the 469
uncertainty of the feature tracking method due to the 15-m grid spacing of the imagery used, 470
and the actual displacement could be less than 9 m a-1. 471
472
The decrease in the elevation of the simulated glacier surface over the 40 years prior to the 473
present day was close to zero at the terminus and increased to 8–10 m in the upper part of the 474
ablation area. The simulated surface lowering shows good agreement both in terms of the 475
16
absolute values and the distribution of surface lowering to that observed for a similar period 476
(1970–2007) which gave an elevation difference of –13.9 ± 2.5 m across the ablation area 477
(Bolch et al., 2011). Integrated mass balance for the simulated present-day glacier was –0.22 478
m w.e. a-1, slightly less negative than but not dissimilar to geodetic mass balance values 479
estimated between 1970 and 2007 as of –0.27 ± 0.08 m w.e. a-1 (Bolch et al., 2011) and 480
between 1992 and 2008 as –0.45 ± 0.52 m w.e. a-1 (Nuimura et al., 2012). 481
482
5.2 Equilibrium Line Altitude 483
The ELA of Khumbu Glacier could be placed in a range from 5200 m to 5600 m assuming 484
that the integrated mass balance is zero (Benn and Lehmkuhl, 2000). However, methods for 485
calculating ELA such as the accumulation-area ratio are difficult to apply to avalanche-fed, 486
debris-covered glaciers for which values appear to be lower (around 0.1–0.4) than those for 487
clean-ice glaciers (0.5–0.6) (Anderson, 2000). Snowline altitude is not a reliable indicator of 488
ELA in high mountain environments, because avalanching, debris cover and high relief affect 489
mass balance such that ELA may differ by several hundred metres from the mean snowline 490
(Benn and Lehmkuhl, 2000). Simulations using the lower estimated ELAs and assuming a net 491
mass balance of zero produced a glacier equivalent to the Late Holocene extent. Simulations 492
optimised to the present-day glacier indicate that ELA is probably about 5800–6000 m (Fig. 493
3b). 494
495
5.3 Sources of uncertainty associated with modelling debris-covered glaciers 496
We used a simple approach to represent the relationship between climate and glacier mass 497
balance to avoid introducing additional uncertainties by making assumptions about the 498
response of meteorological parameters such as monsoon intensity to climate change. 499
Therefore, our results indicate the sensitivity of a debris-covered Himalayan glacier to 500
climate change over the Late Holocene period (1 ka to present). Although iSOSIA captures 501
the dynamics of mountain glaciers, the interaction of high topography with atmospheric 502
circulation systems will affect mass balance (Salerno et al., 2014). Future studies could use 503
downscaled climate model outputs or energy balance modelling to better capture these 504
variables. However, mass balance and meteorological data to support these approaches are 505
scarce for the majority of Himalayan glaciers. 506
507
Differences in the estimated and simulated volume of the present-day glaciers were due to 508
differences in simulated glacier extents. Simulations were designed to give a best fit to 509
17
Khumbu Glacier and produced less extensive ice than observed for Changri Nup and Changri 510
Shar Glaciers (Fig. 7a and b). Sensitivity experiments showed that a range of mass balance 511
values and lapse rates had little impact on these tributaries, suggesting that the mass balance 512
of Khumbu Glacier does not precisely represent that of the tributaries. This mismatch could 513
be due to the differences in hypsometry between glaciers and model calibration to the 514
extreme altitudes in the Western Cwm. 515
516
There are no measurements with which to constrain ice thickness in the Western Cwm, so our 517
estimate of ice thickness is based solely on the slope of the glacier surface derived from the 518
DEM and tuning of values for basal shear stress (IJb) and glacier shape to match geophysical 519
observations (Fig. 3). The IJb values initially used to determine bed topography are within the 520
range simulated using iSOSIA (Fig. 8a and 8b) suggesting that our estimate of bed 521
topography is appropriate. However, calculation of bed topography beneath glaciers and ice 522
sheets remains an outstanding challenge in glaciology, and one that is difficult to resolve in 523
the absence of data describing the basal properties of the glacier. 524
525
The addition of debris to the glacier surface by rock avalanching from the surrounding 526
hillslopes is not represented in our glacier model, but previous studies have demonstrated that 527
large rock avalanches can perturb the terminus position of mountain glaciers (e.g. Menounos 528
et al., 2013; Vacco et al., 2010). Sub-debris ablation is modified by the physical properties of 529
the debris layer, particularly variations in water content and grain size (Collier et al., 2014). 530
Exposed ice cliffs can enhance ablation locally on debris-covered glaciers; at Miage Glacier 531
in the European Alps ice cliffs occupy 1% of the debris-covered area and account for 7% of 532
total ablation (Reid and Brock, 2014). Previous work has hypothesised that ice cliff ablation 533
may be responsible for the comparable rates of mass loss observed for debris-covered and 534
clean-ice glaciers in the Himalaya and Karakoram (Gardelle et al., 2012; Kääb et al., 2012). 535
Mapping the area of debris-covered surfaces occupied by ice cliffs and increasing ablation 536
accordingly could refine our predictions of future glacier change. This would require more 537
detailed topographic data than the 30-m DEM and parameterisation of the processes by which 538
ice cliffs form and decay. As we do not incorporate ice cliffs or supraglacial ponds into our 539
modelling, and as these features are likely to become more widespread as surface lowering 540
continues, our estimates of mass loss from the present day to AD2200 are likely to be 541
cautious. 542
543
18
6. Conclusions 544
Predictions of debris-covered glacier change based either on assumptions about clean-ice 545
glaciers or including static adjustments of ablation rates do not capture the feedbacks 546
amongst mass balance, ice dynamics and debris transport that govern the behaviour of these 547
glaciers, and are unlikely to give reliable results. We present the first dynamic model of the 548
evolution of a debris-covered glacier and demonstrate that including these important 549
feedbacks simulated glacier mass loss by surface lowering rather than terminus recession, and 550
represents the observed response to climate change of debris-covered glaciers. Models such 551
as this that represent the transient processes governing the behaviour of debris-covered 552
glaciers, supported by detailed direct and remotely-sensed observations, are needed to 553
accurately predict glacier change in mountain ranges such as the Himalaya. 554
555
The development of supraglacial debris on Khumbu Glacier in Nepal promoted a reversed 556
mass balance profile across the ablation area, resulting in greatest mass loss after the Little 557
Ice Age (0.5 ka) where debris was absent close to the icefall and least mass loss on the 558
debris-covered tongue. The reduction in ablation across the debris-covered section of the 559
glacier resulted in reduced ice flow and debris export. Khumbu Glacier extends to a lower 560
altitude (4870 m a.s.l. compared to 5160 m a.s.l.) and greater length (15.7 km compared to 561
10.3 km) than would be possible without supraglacial debris. We predict a loss of ice 562
equivalent to 8–10% of the present-day glacier volume by AD2100 with only minor change 563
in glacier area and length, and physical detachment of the debris-covered tongue from the 564
upper active part of the glacier before AD2200. Regional atmospheric warming is likely to 565
result in a similar response from other debris-covered glaciers in the Everest region over the 566
same period. 567
568
569
570
Acknowledgements We thank S. Brocklehurst for critical discussion and reading of the 571
manuscript. Some of this research was undertaken while A.V.R. was supported by a Climate 572
Change Consortium of Wales (C3W) postdoctoral research fellowship at Aberystwyth 573
University. The glacier model simulations were performed on the Iceberg High-Performance 574
Computer at the University of Sheffield. ASTER GDEM is a product of METI and NASA. 575
Two anonymous reviewers are thanked for helpful comments that improved the clarity of this 576
manuscript. 577
19
578
579
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723
Table caption 724
Table 1. Simulated glacier volume, ice thickness and velocity during the Little Ice Age (LIA), 725
22
the present day and predicted for AD2100 under a maximum IPCC warming scenario of 726
1.6°C. 727
728
Figure captions 729
Figure 1. Conceptual model of the development of a debris-covered Himalayan glacier; (a) in 730
balance with climate, and (b) during net mass loss under a warming climate. 731
732
Figure 2. Debris-covered Khumbu Glacier. (a) Photograph of the ablation area of Khumbu 733
Glacier looking downglacier from Kala Pathar showing the elevation difference between the 734
Little Ice Age lateral moraine crests and the glacier surface and relict landslide material that 735
has remained in situ from at least 2003 to 2014. (b) Long profile of 100-m mean swath 736
topography of Khumbu Glacier, and (c) long profile of 100-m mean swath topography of 737
Khumbu Glacier below the confluence with the Changri Nup tributary showing the elevation 738
difference between the glacier surface and the Little Ice Age lateral moraine crest due to mass 739
loss by surface lowering. The lowest point of the terminal moraine is 4670 m a.s.l.. 740
741
Figure 3. (a) Present-day ice thickness of Khumbu Glacier estimated from a DEM 742
constructed for the year 2011 as described in Section 3.1, tuned with available ice thickness 743
measurements from radio-echo sounding (Gades et al., 2000) and gravity observations 744
(Moribayashi, 1978), draped over a shaded-relief map of the estimated bedrock topography 745
used to describe the model domain (EBC = Everest Base Camp). (b) Long profile of Khumbu 746
Glacier showing the range of the ELA based on morphometric calculations and 747
measurements of mass balance from previous studies (Benn and Lehmkuhl, 2000; Bolch et 748
al., 2011; Inoue, 1977; Inoue and Yoshida, 1980), the ELA simulated for the present day 749
glacier, and the range of ELA used to represent IPCC scenarios for AD2100. 750
751
Figure 4. Present-day velocities of Khumbu Glacier calculated using feature tracking of the 752
panchromatic bands of multi-temporal Landsat Operational Land Imager (OLI) imagery. The 753
underlying image was acquired by the Landsat OLI on 4th May 2013 and the white areas 754
denote areas with no data. The glacier outline is defined according to the Randolph Glacier 755
Inventory (GLIMS et al., 2005). Note the termination of the measured active ice (i.e. above 756
the uncertainty in the method) is 5.4 km upglacier from the terminus. The location of this 757
figure and the extent of the Central Himalayan region (red dashed line) are shown in the inset 758
map. 759
23
760
Figure 5. Initial steady-state simulation of Khumbu Glacier during the Late Holocene 761
advance (1 ka) used as a starting point for the Little Ice Age simulations, showing (a) ice 762
thickness, (b) debris thickness, (c) mass balance (in metres of water equivalent per year), and 763
(d) velocities. 764
765
Figure 6. Simulations of Khumbu Glacier as a clean-ice rather than debris-covered glacier. 766
(a) present day ice thickness simulated without a supraglacial debris layer, and (b) present-767
day ice thickness simulated without ablation beneath a debris layer with a 50% reduction in 768
ablation. 769
770
Figure 7. Simulations of Khumbu Glacier during the Little Ice Age (LIA; 0.5 ka) and present 771
day. Results from the iSOSIA model for; (a) ice thickness during the LIA, (b) ice thickness at 772
the present day, and simulated supraglacial debris (c) during the LIA, and (d) at the present 773
day. The fit between the simulated glaciers, the LIA lateral moraine crest, and the present day 774
glacier surface are shown for (e) the LIA and (f) the present day. 775
776
Figure 8. Simulated velocities for Khumbu Glacier (a) during the Little Ice Age, and (b) at 777
the present day [Note log scale for velocity], and simulated basal shear stress (IJb) for Khumbu 778
Glacier (c) during the Little Ice Age, and (d) at the present day. 779
780
Figure 9. Simulations of Khumbu Glacier in AD2100 and AD2200. (a) Simulated ice 781
thickness in AD2100 under the maximum IPCC CMIP5 RCP 4.5 warming scenario 782
equivalent to an increase in temperature of 1.6°C from the present day, and (b) assuming the 783
same warming scenario from the present day, the ice thickness in AD2200 after the active 784
glacier detached from the debris-covered tongue. Differences in ice thickness from the 785
present day simulation in (c) AD2100 and (d) AD2200 [Note the different scales for 786
difference in ice thickness]. Debris thickness in (e) AD2100 and (f) AD2200. The Little Ice 787
Age lateral moraine crest, present day glacier surface and simulated glacier surface for (g) the 788
AD2100 and (h) the AD2200 simulations. 789
